Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
240 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C5×#353 | C2 | semidirect |
| 3. C5×#4545 | C2 | semidirect |
| 8. C5×#874 | C4 | semidirect |
| 11. C4×C5×C3⋊C8 | C4 | semidirect |
| 12. #67541 | C5 | direct (N × H) |
| 15. C5×#353 | D3 | semidirect |
| 28. C3×#353 | C2×C5 | semidirect |
| 29. #4545 | C2×C5 | semidirect |
| 55. #874 | C4×C5 | semidirect |
| 58. C4×C3⋊C8 | C4×C5 | semidirect |
| 72. #353 | C5×D3 | semidirect |
| 157. C3×C5 | #1408 | semidirect |
| 193. C5 | #67541 | direct (N × H) |
| 205. C3 | C5×#1408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#5073 | 2 |
| C3×C5×#353 | 2 |
| C5×#4545 | 2 |
| C5×#1408 | 3 |
| #67541 | 5 |